A few families took a trip to an amusement park together. Tickets cost $$5.50$ each for adults and $$4.00$ each for kids, and the group paid $$50.00$ in total. There were $3$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${5.5x+4y = 50}$ ${x = y-3}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-3}$ for $x$ in the first equation. ${5.5}{(y-3)}{+ 4y = 50}$ Simplify and solve for $y$ $ 5.5y-16.5 + 4y = 50 $ $ 9.5y-16.5 = 50 $ $ 9.5y = 66.5 $ $ y = \dfrac{66.5}{9.5} $ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into ${x = y-3}$ to find $x$ ${x = }{(7)}{ - 3}$ ${x = 4}$ You can also plug ${y = 7}$ into ${5.5x+4y = 50}$ and get the same answer for $x$ ${5.5x + 4}{(7)}{= 50}$ ${x = 4}$ There were $4$ adults and $7$ kids.